The real value of $a$ for which the system of equations $x+ay=0, y+az=0, z+ax=0$ has infinitely many solutions, is :

If $A=\begin{bmatrix}0 & b-a & c-a\\a-b & 0 & c-b\\a-c & b-c & 0\end{bmatrix}$ then the value of $\lvert A \rvert$ is

If $\begin{vmatrix} p-a & 0 & c-r \\ 0 & q-b & c-r \\ a & b & r \end{vmatrix} = 0$, then the value of $\dfrac{p}{p-a} + \dfrac{q}{q-b} + \dfrac{r}{r-c}$ is

The sum of a matrix $A$ and its transpose is $\begin{bmatrix}6 & -1\\ -1 & 4\end{bmatrix}$.

Which of the following statements is true?

The sum of the products of elements of any row with the cofactors of corresponding elements is equal to :

If A is a square matrix of order 3 such that $|A|=2$, then the value of $|adj(adj A)|$ is :

For matrix $A = \begin{bmatrix} 2 & -3 \\ 3 & 4 \end{bmatrix}$ the value of $A^2 - 6A$ is equal to:(where I is an identity matrix of order 2)